Geodesic
Extended $G$-vertex colored partition algebras as centralizer algebras of symmetric groups
Algebra and discrete mathematics, no. 2 (2005), pp. 58-79

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The Partition algebras $P_k(x)$ have been defined in [M1] and [Jo]. We introduce a new class of algebras for every group $G$ called "Extended $G$-Vertex Colored Partition Algebras," denoted by $\widehat{P}_{k}(x,G)$, which contain partition algebras $P_k(x)$, as subalgebras. We generalized Jones result by showing that for a finite group $G$, the algebra $\widehat{P}_{k}(n,G)$ is the centralizer algebra of an action of the symmetric group $S_n$ on tensor space $W^{\otimes k}$, where $W=\mathbb{C}^{n|G|}$. Further we show that these algebras $\widehat{P}_{k}(x,G)$ contain as subalgebras the "$G$-Vertex Colored Partition Algebras ${P_{k}(x,G)}$," introduced in [PK1].
Keywords: centralizer algebra, direct product, wreath product, symmetric group.
Mots-clés : Partition algebra 
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     author = {M. Parvathi and A. Joseph Kennedy},
     title = {Extended $G$-vertex colored partition algebras as centralizer algebras of symmetric groups},
     journal = {Algebra and discrete mathematics},
     pages = {58--79},
     publisher = {mathdoc},
     number = {2},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2005_2_a4/}
}
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M. Parvathi; A. Joseph Kennedy. Extended $G$-vertex colored partition algebras as centralizer algebras of symmetric groups. Algebra and discrete mathematics, no. 2 (2005), pp. 58-79. http://geodesic.mathdoc.fr/item/ADM_2005_2_a4/